Volume 77, Number 5, March 2007
|Number of page(s)||5|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||21 February 2007|
Effect of memory kernels on the speed of reaction-diffusion fronts
Grup de Física Estadística, Departament de Física, Universitat Autònoma de Barcelona - E-08193 Bellaterra, Barcelona, Spain
2 School of Mathematics, The University of Manchester - Manchester M60 1DQ, UK
3 Department of Chemistry, Southern Methodist University - Dallas, TX 75275-0314, USA
Accepted: 18 January 2007
We study the role of a memory kernel, in the constitutive equation for the particle flux, on the speed of propagating fronts in reaction-diffusion systems. We prove for general memory kernels the existence of propagating fronts with a speed bounded by the characteristics of the transport process, even in the fast-reaction limit. This upper bound depends only on the zero-delay value of the memory kernel. To illustrate our results, we consider examples of some functional forms for the memory kernel.
PACS: 87.10.+e – Biological and medical physics: general theory and mathematical aspects / 05.40.-a – Fluctuation phenomena, random processes, noise and Brownian motion / 05.60.Cd – Classical transport
© Europhysics Letters Association, 2007
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